Abstract

We demonstrate parabolic optical pulse generation by manipulating the intensity and phase of individual longitudinal modes of a 40GHz picosecond optical pulse train in the spectral domain. Bright and dark parabolic pulses were generated from a 40GHz mode-locked fiber laser using a 64-channel arrayed waveguide grating pulse shaper. The obtained parabolic pulse, which can easily generate a linear chirping, is useful for a number of applications to optical signal processing applications, including pulse compression and time-domain optical Fourier transformation.

© 2008 Optical Society of America

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  1. K. Tamura and M. Nakazawa, Opt. Lett. 21, 68 (1996).
    [CrossRef] [PubMed]
  2. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
    [CrossRef] [PubMed]
  3. T. Hirooka and M. Nakazawa, Opt. Lett. 29, 498 (2004).
    [CrossRef] [PubMed]
  4. B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, Electron. Lett. 42, 965 (2006).
    [CrossRef]
  5. J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
    [CrossRef]
  6. T. Hirooka and M. Nakazawa, in International Conference on Quantum Electronics and the Pacific Rim Conference on Lasers and Electro-Optics (IQEC/CLEO-PR 2005) (2005), paper CFJ3-4-INV.
    [PubMed]
  7. F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, IEEE Photon. Technol. Lett. 18, 829 (2006).
    [CrossRef]
  8. T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, in Optical Fiber Communication Conference (OFC 2007) (2007), paper JWA58.
  9. K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
    [CrossRef]
  10. K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, Electron. Lett. 40, 537 (2004).
    [CrossRef]
  11. Z. Jiang, D. S. Seo, D. E. Leaird, and A. M. Weiner, Opt. Lett. 30, 1557 (2005).
    [CrossRef] [PubMed]
  12. M. Yoshida, K. Kasai, and M. Nakazawa, IEEE J. Quantum Electron. 43, 704 (2007).
    [CrossRef]

2007 (3)

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, in Optical Fiber Communication Conference (OFC 2007) (2007), paper JWA58.

M. Yoshida, K. Kasai, and M. Nakazawa, IEEE J. Quantum Electron. 43, 704 (2007).
[CrossRef]

2006 (2)

B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, Electron. Lett. 42, 965 (2006).
[CrossRef]

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, IEEE Photon. Technol. Lett. 18, 829 (2006).
[CrossRef]

2005 (2)

T. Hirooka and M. Nakazawa, in International Conference on Quantum Electronics and the Pacific Rim Conference on Lasers and Electro-Optics (IQEC/CLEO-PR 2005) (2005), paper CFJ3-4-INV.
[PubMed]

Z. Jiang, D. S. Seo, D. E. Leaird, and A. M. Weiner, Opt. Lett. 30, 1557 (2005).
[CrossRef] [PubMed]

2004 (2)

T. Hirooka and M. Nakazawa, Opt. Lett. 29, 498 (2004).
[CrossRef] [PubMed]

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, Electron. Lett. 40, 537 (2004).
[CrossRef]

2000 (1)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

1999 (1)

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

1996 (1)

Billet, C.

B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, Electron. Lett. 42, 965 (2006).
[CrossRef]

Dudley, J. M.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, Electron. Lett. 42, 965 (2006).
[CrossRef]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Fermann, M. E.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Ferriere, R.

B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, Electron. Lett. 42, 965 (2006).
[CrossRef]

Finot, C.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

Goh, T.

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

Harvey, J. D.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Hirooka, T.

T. Hirooka and M. Nakazawa, in International Conference on Quantum Electronics and the Pacific Rim Conference on Lasers and Electro-Optics (IQEC/CLEO-PR 2005) (2005), paper CFJ3-4-INV.
[PubMed]

T. Hirooka and M. Nakazawa, Opt. Lett. 29, 498 (2004).
[CrossRef] [PubMed]

Ibsen, M.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, in Optical Fiber Communication Conference (OFC 2007) (2007), paper JWA58.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, IEEE Photon. Technol. Lett. 18, 829 (2006).
[CrossRef]

Jiang, Z.

Kasai, K.

M. Yoshida, K. Kasai, and M. Nakazawa, IEEE J. Quantum Electron. 43, 704 (2007).
[CrossRef]

Kibler, B.

B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, Electron. Lett. 42, 965 (2006).
[CrossRef]

Kominato, T.

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, Electron. Lett. 40, 537 (2004).
[CrossRef]

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

Kruglov, V. I.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Lacourt, P. A.

B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, Electron. Lett. 42, 965 (2006).
[CrossRef]

Larger, L.

B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, Electron. Lett. 42, 965 (2006).
[CrossRef]

Leaird, D. E.

Millot, G.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

Nakazawa, M.

M. Yoshida, K. Kasai, and M. Nakazawa, IEEE J. Quantum Electron. 43, 704 (2007).
[CrossRef]

T. Hirooka and M. Nakazawa, in International Conference on Quantum Electronics and the Pacific Rim Conference on Lasers and Electro-Optics (IQEC/CLEO-PR 2005) (2005), paper CFJ3-4-INV.
[PubMed]

T. Hirooka and M. Nakazawa, Opt. Lett. 29, 498 (2004).
[CrossRef] [PubMed]

K. Tamura and M. Nakazawa, Opt. Lett. 21, 68 (1996).
[CrossRef] [PubMed]

Ng, T. T.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, in Optical Fiber Communication Conference (OFC 2007) (2007), paper JWA58.

Okamoto, K.

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, Electron. Lett. 40, 537 (2004).
[CrossRef]

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

Parmigiani, F.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, in Optical Fiber Communication Conference (OFC 2007) (2007), paper JWA58.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, IEEE Photon. Technol. Lett. 18, 829 (2006).
[CrossRef]

Petropoulos, P.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, in Optical Fiber Communication Conference (OFC 2007) (2007), paper JWA58.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, IEEE Photon. Technol. Lett. 18, 829 (2006).
[CrossRef]

Richardson, D. J.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, in Optical Fiber Communication Conference (OFC 2007) (2007), paper JWA58.

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, IEEE Photon. Technol. Lett. 18, 829 (2006).
[CrossRef]

Seo, D. S.

Shibata, T.

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, Electron. Lett. 40, 537 (2004).
[CrossRef]

Takahashi, H.

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, Electron. Lett. 40, 537 (2004).
[CrossRef]

Takiguchi, K.

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, Electron. Lett. 40, 537 (2004).
[CrossRef]

Tamura, K.

Thomsen, B. C.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Weiner, A. M.

Yamada, H.

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

Yoshida, M.

M. Yoshida, K. Kasai, and M. Nakazawa, IEEE J. Quantum Electron. 43, 704 (2007).
[CrossRef]

Zhang, Z.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, in Optical Fiber Communication Conference (OFC 2007) (2007), paper JWA58.

Electron. Lett. (3)

B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, Electron. Lett. 42, 965 (2006).
[CrossRef]

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, Electron. Lett. 35, 733 (1999).
[CrossRef]

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, Electron. Lett. 40, 537 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Yoshida, K. Kasai, and M. Nakazawa, IEEE J. Quantum Electron. 43, 704 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, IEEE Photon. Technol. Lett. 18, 829 (2006).
[CrossRef]

Nat. Phys. (1)

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Other (2)

T. Hirooka and M. Nakazawa, in International Conference on Quantum Electronics and the Pacific Rim Conference on Lasers and Electro-Optics (IQEC/CLEO-PR 2005) (2005), paper CFJ3-4-INV.
[PubMed]

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, in Optical Fiber Communication Conference (OFC 2007) (2007), paper JWA58.

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Figures (6)

Fig. 1
Fig. 1

(a) Intensity profile and (b) power spectrum of 40 GHz bright parabolic pulse.

Fig. 2
Fig. 2

(a) Intensity profile and (b) power spectrum of 40 GHz dark parabolic pulse.

Fig. 3
Fig. 3

Experimental setup for parabolic pulse generation using an AWG pulse shaper.

Fig. 4
Fig. 4

Transmission spectrum of parabola-shaping optical filter for preshaping. The dotted curve shows the ideal spectrum of a bright parabolic pulse.

Fig. 5
Fig. 5

(a) Waveform and (b) optical spectrum of 40 GHz bright parabolic pulse.

Fig. 6
Fig. 6

(a) Waveform and (b) optical spectrum of 40 GHz dark parabolic pulse.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

u b ( t ) = 1 ( t T 0 ) 2 , t T 0 ,
u ̂ b ( ω ) = ( π ω ) J 1 ( ω T 0 ) .
u d ( t ) = ( 1 ) n ( t 2 n T 0 ) T 0 , ( 2 n 1 ) T 0 t < ( 2 n + 1 ) T 0 ,
u ̂ d ( ω ) = 2 sin ( 2 ω T 0 ) ω ( 2 ω 2 ) ( cos 2 ω T 0 1 ) .

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